This is NOT how I learned math before a few years ago. I was lucky to be experiencing math frequently enough that I didn't `forget` too much of it. I sporadically made realizations only by the enormous talent and persistence of my math teachers, the creators of math videos, and the writers of books and competitions. In effort to have more consistent and significant steps in my understanding and ability, I started taking digital notes about 5 years ago. I wasted the first few years with inefficient techniques and proprietary formats, but have 0. Get ready to add to knowledge - open the programs - PDF Reader - PKM (Obsidian) - Drawing App (or Paper) - arrange the windows - take a deep breath and... 1. Read, deeply; add notes, frequently - (re-)read until understood - lookup everything unknown, and add it to PKM - paraphrase everything that isn't just trivial info or examples - Make many small notes - The smaller the piece of knowledge, the more places it fits. - The more places it fits, the more it is used - The more it is used, the more it is understood. - The more it is understood, the more it will be revised - The most revised notes are the ones that are closest to both: - Truthfulness and - Usefulness 2. Generalize, carefully; link generously - Connecting truths does not immediately need to generate new ones - With infinite resources and power, the benefits of generalization do not outweigh the risks of writing useless/truthless statements - Links show connections that may turn into new ideas - They also increase mouse navigability, useful for readers 3. Evaluate - Quantity - Number and density of notes and links - Is anything getting in the way of your output? - Making lots of diagrams will decrease output numbers - Quality - What do you admire about the notes that make you proudest? - (These are often the ones with the most links, or most carefully formatted) - Are some notes totally useless? - Try revising - add breaks, bullets - cut up into smaller notes - research more to see if you got the point - Try linking to and from them - Or know when to trash them and not make similar mistakes - I have *trashed* **half** as many notes as I have *kept* 4. Publish (can be done earlier) - Share notes with people who will find them useful - Ask for feedback from a variety of people. - People with more experience - Will give you more reassurance of the direction you take - People with less experience - Will motivate further elaboration and exploration